Tuning of a musical instrument traditionally involves a first player listening to a reference note, which may be the note sounded by one or more other players of an ensemble, and adjusting the first player's instrument until the corresponding note is consonant with the reference note. Detection of correct intonation involves a subconscious comparison of the two notes until the combination of the two notes are in tune with each other.
The determination of correct intonation is a skill which is acquired as part of the player's basic musicianship training and which is acquired only after long hours of practice. As with many acquired skills, the accuracy of the intonation which results is a combination of the inherent talent of the performer and the diligence with which the task is pursued.
There have been numerous prior art attempts to provide electromechanical, mechanical or electronic apparatus for use as tuning aids which can detect the presence or absence of the desired intonation characteristics. Musicians are greatly assisted by the use of such tuning aids. For example, professional players can benefit from comparison of their intonation with the theoretically perfect standard.
For example, one class of prior art tuning aids are frequency meters which employ period measuring circuits to detect a zero crossing of the output of a suitable transducer. The inverse of the period may then be computed and the frequency of the tone thus determined and displays. Such instruments can give quite accurate results, but suffer from a disadvantage and limitation that the displayed value has little meaning to a musician who thinks not in terms of physical units but rather in terms of subjective cycle acoustic phenomenon such as pitch. A further disadvantage and limitation of such devices is that the detected waveform contains not only the fundamental frequency but also harmonic frequencies of the fundamental frequency. Therefore, the period measuring circuit may develop an error when encountering zero crossings of the transducer output which are caused by the summation of the harmonic frequencies in the fundamental frequency.
For example, Moravec, et al., U.S. Pat. No. 4,354,418, disclose an automatic note analyzer which computes the fundamental frequency from the time period of the output signal from a transducer. A data count is obtained by counting the number of CPU clock pulses counted within a measurement period extending over P consecutive cycles of the input signal, or data count equals P times C.sub.1, where C.sub.1 equals the period of the input signal. The measurement period should extend for at least two cycles of the input signal. A number of sequential data counts similar to the first data count are then taken. These data counts are then analyzed to determine whether a consistent pattern can be found. In particular, N separate data counts which are equal to one another, within a tolerance of about 3%, are attempted to be found. Once N consistent data counts are found, then a variable K is set equal to the sum of these N data counts. Thus, K is a variable which corresponds to the sum of a selected number of N consistent data counts. Since the time period C.sub.1 is not actually a constant value, the variable K is a function of three variables: (1) the time delay between adjacent zero crossings, (2) the duration of the measurement period of a single data count in terms of the number of zero crossings which occur between the starting and stopping of the counter, and (3) the number of data counts which are summed to determine K.
Once an initial value for the variable K has been determined, K is then normalized to place it within a desired range. The normalization is accomplished by multiplying or dividing as necessary by factors of 2 until it falls within the desired range. For example, if the value of K is lower than the minimum accepted value, K is doubled. If K is still below the minimum acceptable value then it is doubled again. Conversely, if K is greater than the maximum allowed value then the value of K is divided by 2 and so forth. In this way, the variable K is normalized to fall within the desired range. Of course this desired range is the expected value.
The normalized value of K is then averaged with previous calculated values of K to smooth out fluctuations. For example, the current value of K may be summed with 15 immediately preceding values of K and the summed divided by 16 to recursively generate an average. The variable T is then equal to the recursively averaged K divided by N. T is a measure of the expected data count for measurement periods lasting over P cycles of the input signal. The variable T is used as a target signal to define a window which is used to screen incoming data to ascertain whether that incoming data is consistent with previously measured values of the data count and thereby to screen out erroneous measurements.
In addition, the recursive average of K is used to determine the musical note corresponding to the input signal. In particular, the recursively averaged K is compared with the look-up table which lists values for the recursively averaged K at the halfway points between adjacent semi-tone. In this way, the semitone closest to the recursively averaged K is determined. In addition, the difference between recursively averaged K and the table entry for the nearest semitone is determined as the fractional deviation of the recursively averaged K from the nearest semitone in cents.
A disadvantage and limitation of the apparatus disclosed in Moravec, et al., is that the computations to compute K or frequency appear to be sensitive to large amplitude harmonics of the fundamental frequency. In calculating K, it is assumed that interrupts will occur at the fundamental frequency of the output signal from the transducer. However, relatively large amplitude harmonics which occur will cause substantial measurement errors in this fundamental frequency. Since this error will not always be in a factor of two, the calculated fundamental frequency may be in gross error.
Other types of electronic apparatus use a comparison of a known frequency standard, such as the output frequency of a crystal controlled oscillator, with the frequency of the unknown signal being measured. Both signals are electronically conditioned to provide a substantially pure sine waveform before they are applied to the vertical and horizontal deflection plates of a cathode ray tube oscilloscope. When the notes are identical in frequency, a circular "Lissajous" pattern is formed on the screen. When sharp or flat the Lissajous pattern will appear to rotate at a rate which is determined by the magnitude of the departure of the frequency of the unknown signal from the frequency of the reference signal.
A similar oscilloscope based device employs an oscilloscope having a known horizontal sweep rate. The horizontal sweep rate is then compared with an unknown signal input. When the signal is properly synchronized, a stationary waveform will appear on the oscilloscope screen. When the note represented by the unknown signal is slightly too sharp, the pattern appears to move to the left. Conversely, when the note is slightly too flat, the pattern appears to move to the right.
The indications available from these oscilloscope based instruments are ambiguous to the user in that the degree of the inaccuracy of the incoming pitch cannot be readily be determined. In the case of the first type of oscilloscope display described, it is difficult to determine both polarity (sharp or flat) and the degree of departure from the theoretical perfect intonation. Since the user is unable to determine the needed information by merely viewing the oscilloscope screen, he can never be absolutely sure of his intonation. Moreover, as a training aid, these devices are disadvantageously limited in that they do not readily indicate in which direction the pitch of the unknown signal must be varied in order to bring it close to the theoretically correct pitch.
To make the displays more readable, LED diodes in a linear array may be used. For example, in Roses. U.S. Pat. No. 4,434,697, there is disclosed a tuning device wherein an acoustic signal is used to develop an electrical input signal. The input signal is applied to a plurality of low pass filters. The signal from the lowest cut-off frequency low pass filter which passes the signal is utilized. After filtering, a high frequency clock count is obtained to determine the time period of the signal chosen. An entry and a look-up table in computer memory is selected as being the closest to determine time period. An LED display is used to determine visually if the time period of chosen signal is above or below the selected entry in the look-up table.